Mathematical Psychology

This project investigates mathematical psychology's historical and philosophical foundations to clarify its distinguishing characteristics and relationships to adjacent fields. Through gathering primary sources, histories, and interviews with researchers, author Prof. Colin Allen - University of Pittsburgh [1, 2, 3] and his students Osman Attah, Brendan Fleig-Goldstein, Mara McGuire, and Dzintra Ullis have identified three central questions:

What makes the use of mathematics in mathematical psychology reasonably effective, in contrast to other sciences like physics-inspired mathematical biology or symbolic cognitive science?
How does the mathematical approach in mathematical psychology differ from other branches of psychology, like psychophysics and psychometrics?
What is the appropriate relationship of mathematical psychology to cognitive science, given diverging perspectives on aligning with this field?

Preliminary findings emphasize data-driven modeling, skepticism of cognitive science alignments, and early reliance on computation. They will further probe the interplay with cognitive neuroscience and contrast rational-analysis approaches. By elucidating the motivating perspectives and objectives of different eras in mathematical psychology's development, they aim to understand its past and inform constructive dialogue on its philosophical foundations and future directions. This project intends to provide a conceptual roadmap for the field through integrated history and philosophy of science.

The Project: Integrating History and Philosophy of Mathematical Psychology

This project aims to integrate historical and philosophical perspectives to elucidate the foundations of mathematical psychology. As Norwood Hanson stated, history without philosophy is blind, while philosophy without history is empty. The goal is to find a middle ground between the contextual focus of history and the conceptual focus of philosophy.

The team acknowledges that all historical accounts are imperfect, but some can provide valuable insights. The history of mathematical psychology is difficult to tell without centering on the influential Stanford group. Tracing academic lineages and key events includes part of the picture, but more context is needed to fully understand the field's development.

The project draws on diverse sources, including research interviews, retrospective articles, formal histories, and online materials. More interviews and research will further flesh out the historical and philosophical foundations. While incomplete, the current analysis aims to identify important themes, contrasts, and questions that shaped mathematical psychology's evolution. Ultimately, the goal is an integrated historical and conceptual roadmap to inform contemporary perspectives on the field's identity and future directions.

The Rise of Mathematical Psychology

The history of efforts to mathematize psychology traces back to the quantitative imperative stemming from the Galilean scientific revolution. This imprinted the notion that proper science requires mathematics, leading to "physics envy" in other disciplines like psychology.

Many early psychologists argued psychology needed to become mathematical to be scientific. However, mathematizing psychology faced complications absent in the physical sciences. Objects in psychology were not readily present as quantifiable, provoking heated debates on whether psychometric and psychophysical measurements were meaningful.

Nonetheless, the desire to develop mathematical psychology persisted. Different approaches grappled with determining the appropriate role of mathematics in relation to psychological experiments and data. For example, Herbart favored starting with mathematics to ensure accuracy, while Fechner insisted experiments must come first to ground mathematics.

Tensions remain between data-driven versus theory-driven mathematization of psychology. Contemporary perspectives range from psychometric and psychophysical stances that foreground data to measurement-theoretical and computational approaches that emphasize formal models.

Elucidating how psychologists negotiated to apply mathematical methods to an apparently resistant subject matter helps reveal the evolving role and place of mathematics in psychology. This historical interplay shaped the emergence of mathematical psychology as a field.

The Distinctive Mathematical Approach of Mathematical Psychology

What sets mathematical psychology apart from other branches of psychology in its use of mathematics?

Several key aspects stand out:

Advocating quantitative methods broadly. Mathematical psychology emerged partly to push psychology to embrace quantitative modeling and mathematics beyond basic statistics.
Drawing from diverse mathematical tools. With greater training in mathematics, mathematical psychologists utilize more advanced and varied mathematical techniques like topology and differential geometry.
Linking models and experiments. Mathematical psychologists emphasize tightly connecting experimental design and statistical analysis, with experiments created to test specific models.
Favoring theoretical models. Mathematical psychology incorporates "pure" mathematical results and prefers analytic, hand-fitted models over data-driven computer models.
Seeking general, cumulative theory. Unlike just describing data, mathematical psychology aspires to abstract, general theory supported across experiments, cumulative progress in models, and mathematical insight into psychological mechanisms.

So while not unique to mathematical psychology, these key elements help characterize how its use of mathematics diverges from adjacent fields like psychophysics and psychometrics. Mathematical psychology carved out an identity embracing quantitative methods but also theoretical depth and broad generalization.

Situating Mathematical Psychology Relative to Cognitive Science

What is the appropriate perspective on mathematical psychology's relationship to cognitive psychology and cognitive science? While connected historically and conceptually, essential distinctions exist.

Mathematical psychology draws from diverse disciplines that are also influential in cognitive science, like computer science, psychology, linguistics, and neuroscience. However, mathematical psychology appears more skeptical of alignments with cognitive science.

For example, cognitive science prominently adopted the computer as a model of the human mind, while mathematical psychology focused more narrowly on computers as modeling tools.

Additionally, mathematical psychology seems to take a more critical stance towards purely simulation-based modeling in cognitive science, instead emphasizing iterative modeling tightly linked to experimentation.

Overall, mathematical psychology exhibits significant overlap with cognitive science but strongly asserts its distinct mathematical orientation and modeling perspectives. Elucidating this complex relationship remains an ongoing project, but preliminary analysis suggests mathematical psychology intentionally diverged from cognitive science in its formative development.

This establishes mathematical psychology's separate identity while retaining connections to adjacent disciplines at the intersection of mathematics, psychology, and computation.

Looking Ahead: Open Questions and Future Research

This historical and conceptual analysis of mathematical psychology's foundations has illuminated key themes, contrasts, and questions that shaped the field's development. Further research can build on these preliminary findings.

Additional work is needed to flesh out the fuller intellectual, social, and political context driving the evolution of mathematical psychology. Examining the influences and reactions of key figures will provide a richer picture.

Ongoing investigation can probe whether the identified tensions and contrasts represent historical artifacts or still animate contemporary debates. Do mathematical psychologists today grapple with similar questions on the role of mathematics and modeling?

Further analysis should also elucidate the nature of the purported bidirectional relationship between modeling and experimentation in mathematical psychology. As well, clarifying the diversity of perspectives on goals like generality, abstraction, and cumulative theory-building would be valuable.

Finally, this research aims to spur discussion on philosophical issues such as realism, pluralism, and progress in mathematical psychology models. Is the accuracy and truth value of models an important consideration or mainly beside the point? And where is the field headed - towards greater verisimilitude or an indefinite balancing of complexity and abstraction?

By spurring reflection on this conceptual foundation, this historical and integrative analysis hopes to provide a roadmap to inform constructive dialogue on mathematical psychology's identity and future trajectory.

The SDTEST^®

The SDTEST^® is a simple and fun tool to uncover our unique motivational values that use mathematical psychology of varying complexity.

The SDTEST^® helps us better understand ourselves and others on this lifelong path of self-discovery.

Here are reports of polls which SDTEST^® makes:

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Below you can read an abridged version of the results of our VUCA poll “Fears“. The full version of the results is available for free in the FAQ section after login or registration.

Курку

сызымнарын Correlation

VUCA

Корреляция коэффициенты тәнкыйтьли кыйммәтле

Нормаль тарату, Уильям Меали Госсет (студент) r = 0.0353

Спирман белән гадәти булмаган тарату r = 0.0014

Нәтиҗәне генә күрсәтегез > r = 0.0353

Тарату	Нормаль булмаган	Нормаль	Нормаль булмаган	Нормаль	Нормаль	Нормаль	Нормаль	Нормаль
Барлык сораулар Барлык сораулар Минем иң зур куркуым
Минем иң зур куркуым
Answer 1	-	Зәгыйфь уңай 0.0297	Зәгыйфь уңай 0.0298	Зәгыйфь тискәре -0.0106	Зәгыйфь уңай 0.0970	Зәгыйфь уңай 0.0325	Зәгыйфь тискәре -0.0019	Зәгыйфь тискәре -0.1558
Answer 2	-	Зәгыйфь уңай 0.0188	Зәгыйфь уңай 0.0076	Зәгыйфь тискәре -0.0360	Зәгыйфь уңай 0.0711	Зәгыйфь уңай 0.0387	Зәгыйфь уңай 0.0082	Зәгыйфь тискәре -0.1011
Answer 3	-	Зәгыйфь уңай 0.0026	Зәгыйфь тискәре -0.0170	Зәгыйфь тискәре -0.0443	Зәгыйфь тискәре -0.0458	Зәгыйфь уңай 0.0547	Зәгыйфь уңай 0.0808	Зәгыйфь тискәре -0.0270
Answer 4	-	Зәгыйфь уңай 0.0332	Зәгыйфь уңай 0.0285	Зәгыйфь тискәре -0.0006	Зәгыйфь уңай 0.0155	Зәгыйфь уңай 0.0276	Зәгыйфь уңай 0.0105	Зәгыйфь тискәре -0.0917
Answer 5	-	Зәгыйфь уңай 0.0122	Зәгыйфь уңай 0.1193	Зәгыйфь уңай 0.0095	Зәгыйфь уңай 0.0721	Зәгыйфь уңай 0.0057	Зәгыйфь тискәре -0.0083	Зәгыйфь тискәре -0.1687
Answer 6	-	Зәгыйфь уңай 0.0044	Зәгыйфь уңай 0.0005	Зәгыйфь тискәре -0.0582	Зәгыйфь тискәре -0.0004	Зәгыйфь уңай 0.0210	Зәгыйфь уңай 0.0830	Зәгыйфь тискәре -0.0418
Answer 7	-	Зәгыйфь уңай 0.0242	Зәгыйфь уңай 0.0368	Зәгыйфь тискәре -0.0521	Зәгыйфь тискәре -0.0234	Зәгыйфь уңай 0.0403	Зәгыйфь уңай 0.0568	Зәгыйфь тискәре -0.0597
Answer 8	-	Зәгыйфь уңай 0.0707	Зәгыйфь уңай 0.0781	Зәгыйфь тискәре -0.0244	Зәгыйфь уңай 0.0140	Зәгыйфь уңай 0.0303	Зәгыйфь уңай 0.0137	Зәгыйфь тискәре -0.1334
Answer 9	-	Зәгыйфь уңай 0.0564	Зәгыйфь уңай 0.1531	Зәгыйфь уңай 0.0127	Зәгыйфь уңай 0.0769	Зәгыйфь тискәре -0.0136	Зәгыйфь тискәре -0.0495	Зәгыйфь тискәре -0.1752
Answer 10	-	Зәгыйфь уңай 0.0711	Зәгыйфь уңай 0.0700	Зәгыйфь тискәре -0.0127	Зәгыйфь уңай 0.0246	Зәгыйфь уңай 0.0363	Зәгыйфь тискәре -0.0156	Зәгыйфь тискәре -0.1273
Answer 11	-	Зәгыйфь уңай 0.0542	Зәгыйфь уңай 0.0488	Зәгыйфь уңай 0.0086	Зәгыйфь уңай 0.0078	Зәгыйфь уңай 0.0162	Зәгыйфь уңай 0.0315	Зәгыйфь тискәре -0.1248
Answer 12	-	Зәгыйфь уңай 0.0281	Зәгыйфь уңай 0.0929	Зәгыйфь тискәре -0.0325	Зәгыйфь уңай 0.0361	Зәгыйфь уңай 0.0276	Зәгыйфь уңай 0.0365	Зәгыйфь тискәре -0.1482
Answer 13	-	Зәгыйфь уңай 0.0643	Зәгыйфь уңай 0.0916	Зәгыйфь тискәре -0.0418	Зәгыйфь уңай 0.0237	Зәгыйфь уңай 0.0425	Зәгыйфь уңай 0.0239	Зәгыйфь тискәре -0.1558
Answer 14	-	Зәгыйфь уңай 0.0697	Зәгыйфь уңай 0.1017	Зәгыйфь уңай 0.0149	Зәгыйфь тискәре -0.0062	Зәгыйфь тискәре -0.0087	Зәгыйфь тискәре -0.0002	Зәгыйфь тискәре -0.1161
Answer 15	-	Зәгыйфь уңай 0.0603	Зәгыйфь уңай 0.1299	Зәгыйфь тискәре -0.0379	Зәгыйфь уңай 0.0163	Зәгыйфь тискәре -0.0091	Зәгыйфь уңай 0.0164	Зәгыйфь тискәре -0.1204
Answer 16	-	Зәгыйфь уңай 0.0691	Зәгыйфь уңай 0.0221	Зәгыйфь тискәре -0.0305	Зәгыйфь тискәре -0.0515	Зәгыйфь уңай 0.0750	Зәгыйфь уңай 0.0187	Зәгыйфь тискәре -0.0696

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[1] https://twitter.com/wileyprof

[2] https://colinallen.dnsalias.org

[3] https://philpeople.org/profiles/colin-allen

2023.10.13

Валерий Косенко

Продукция хуҗасы SAAA PAME проекты SDTEST®

Валерий 1993 елда социаль педагог-психолог буларак квалификацияләнде һәм шуннан соң проект белән аның белемен проект кулланды.
Валерий Мастер дәрәҗәсе һәм проект менеджеры алды 2013. Хуҗа программасы вакытында ул проект юлын (GPM GESELLLSSCASCHAFT Füjeptaneschaft FüjeptAnament FüjeptAnament Fürult динамикасы белән танышты.
Валерий валерий төрле спираль динамикага тестлар алып, аның белемен һәм тәҗрибәсен SDTEST версиясен җайлаштыру өчен кулланды.
Валерий - V.u.S.Аның билгесезлеген өйрәнү авторы. Психологиядә спираль динамика һәм математик статистика ярдәмендә концепция, 20 дән артык халыкара сайлау.

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